10k^2=54-12k

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Solution for 10k^2=54-12k equation:


Simplifying
10k2 = 54 + -12k

Solving
10k2 = 54 + -12k

Solving for variable 'k'.

Reorder the terms:
-54 + 12k + 10k2 = 54 + -12k + -54 + 12k

Reorder the terms:
-54 + 12k + 10k2 = 54 + -54 + -12k + 12k

Combine like terms: 54 + -54 = 0
-54 + 12k + 10k2 = 0 + -12k + 12k
-54 + 12k + 10k2 = -12k + 12k

Combine like terms: -12k + 12k = 0
-54 + 12k + 10k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 6k + 5k2) = 0

Factor a trinomial.
2((-3 + -1k)(9 + -5k)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3

Subproblem 2

Set the factor '(9 + -5k)' equal to zero and attempt to solve: Simplifying 9 + -5k = 0 Solving 9 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5k = 0 + -9 -5k = 0 + -9 Combine like terms: 0 + -9 = -9 -5k = -9 Divide each side by '-5'. k = 1.8 Simplifying k = 1.8

Solution

k = {-3, 1.8}

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